A character has access to a roc egg. I would like to work out at what point it could be ridden, and when it stops being a cute bird and turns into a man-eating monster that locals might object to having arrive with the party. How quickly would it grow?

3 Answers
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I had a look at the Emu (as one of the largest birds alive today) and their chicks are full-grown within 5-6 months, they are still looked after their father during this time (up to seven months) so could be considered "young" during this stage. They can leave the nest within a few days so they quickly become semi-independant.

Given the size of a roc this may stretch out a bit more; but even so within a year the party are going to have themselves a massive beast that's easily capable of carrying a character, and since most animals breed once a year that's going to be the longest marker for age.

So going from this; I'd roughly extropolate:

Cute and fluffy chicks: Up to a week. Awww, it ate your finger.
Mobile and up to the size of a pony: One week to one month.
Mobile and dangerous, growing to the size of an elephant but still "young": One month to eight months.
From this point on the beast should be able to be "ridden" to some degree, i.e. training to cope with humans and loads on it's back should be done ready for it to have some hapless lunatic strapped to it's back.
Fully grown and a danger to all and sundry: One year.

This actually doesn't have an answer! Here's some background explaining why:

The Savage Worlds entry on the roc doesn't describe their life-cycle, so there's no Savage Worlds "canon" to answer this.

Outside of Savage Worlds, the Roc is a beast of Arabian mythology so there's no reliable, single source to go back to for more details about the Roc.

Furthermore, all versions of the mythological Roc held that it's a unique creature, not a species, so myths about the Roc aren't even useful for answering a question about a game-creature species of roc.

Savage Worlds undoubtedly contains the roc-as-species because Dungeons & Dragons does. However, even the edition of D&D that had the most details on the ecology and habits of creatures (AD&D 2nd edition) doesn't bother to mention how long hatchlings take to mature.

That means it's up to you! There are a few ways you can decide this.

Decide What's convenient for the game and do that.

If you want this baby roc to require some serious investment on the part of the owner, then make it a long time, like a year. If the player isn't interested in dealing with feeding this monstrous bird tonnes of meat each day, every day for a year, then maybe little Billy isn't ready to be responsible for a pet. Maybe they should start with a pony or a miniature giant space hamster.

If you just want to skip to the giant bird–riding fun, then make it relatively quick.

Try to figure out what "makes sense". Some things to consider:

The roc is huge. An elephant takes 10-12 years to reach young adulthood, and a roc is an order of magnitude larger, so you could justifiably say they take 20 or more years to reach full maturity!

On the other hand, a roc is a bird and thus has considerably less mass for its bulk, so bringing the age of maturity down into elephant range makes some sense.

A roc is also a meat-eating predator, and as such must and can grow more quickly than a slow herbivore, so you could reduce it again down into the range of a year or two to reach young adulthood.

Roc could either be huge "normal" creatures or magical beasts. If you decide that rocs in your world are magical beasts, then you could reasonably increase or decrease how long it takes them to mature as you see fit.

So, how long it takes hatchling rocs to mature into young adults could take anywhere from "not applicable" (for the unique Roc) to 20+ years, and anywhere in between.

One approach would be to ask yourself how quickly does the story require it to grow? If it isn't explicitly described in the 50 Fathoms rules, then my feeling is that it would be open to interpretation, and that you should do whatever is needed to make an interesting adventure for the Roc's owner.